Question

What is the solution of the system of equations? *hint - multiply each term in one of the equations by a common factor to create opposites that cancel out.

4x - 3y = 15
x y = 2

Answer 1

To solve the system of equations 4x - 3y = 15 and xy = 2, we can multiply the second equation by a common factor to create opposites that cancel out. Adding the equations together gives us a simplified equation in terms of y and x. Finally, we can substitute the value of xy into the simplified equation to find the value of y.

Step-by-step explanation:

To solve the system of equations 4x - 3y = 15 and xy = 2, we can use the hint provided by multiplying the second equation by 2 to make the coefficients of x equal in both equations. This gives us 4x - 3y = 15 and 2xy = 4. Now, we can add the two equations together to eliminate the variable x.

When we add the equations, the terms 4x and -4x cancel each other out, leaving us with -3y + 2xy = 15 + 4. Simplifying further, we get -3y + 2xy = 19. Now, we can factor out y to get y(-3 + 2x) = 19.

Since we know that xy = 2, we can substitute 2 for xy in the equation y(-3 + 2x) = 19. This gives us y(-3 + 2x) = 19. Dividing both sides by (-3 + 2x), we find y = 19/(-3 + 2x).